Question

The ratio of effective length of a column and minimum radius of gyration of its cross-sectional area is known as

• A. Crippling factor
• B. Buckling factor
• C. Slenderness ratio
• D. Load factor

Hint:

The Slenderness Ratio ($\lambda = L_{eff} / k_{min}$) is the single most important parameter in column buckling analysis.
It combines information about the column's length, its end supports, and its cross-sectional shape into one number that predicts its susceptibility to buckling.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the definition of a specific ratio used in column analysis.

Step 2: Key Formula or Approach:
The question describes the ratio:
\[ \frac{\text{Effective Length}}{\text{Minimum Radius of Gyration}} \]

Step 3: Detailed Explanation:
This is the precise definition of the

Slenderness Ratio, commonly denoted by $\lambda$ (lambda) or SR.
\[ \lambda = \frac{L_{eff}}{k_{min}} \] The slenderness ratio is a crucial dimensionless number that determines a column's behavior under compression. As explained in question 131, it is used to classify a column as short, intermediate, or long, which in turn determines its failure mode (crushing or buckling). A high slenderness ratio indicates a slender column that is prone to buckling.
- Crippling factor and buckling factor are less standard terms, sometimes used to refer to the load itself or related parameters, but they do not define this specific ratio.
- Load factor is a term used in structural design to account for uncertainties in loads, and is unrelated to column geometry.

Step 4: Final Answer:
The ratio of the effective length of a column and the minimum radius of gyration of its cross-sectional area is known as the slenderness ratio.